lecture25.pdf

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1. Session 25 ICS 211 Priority Queues
2. Memory Upload • Priority queues • Heap implementation • Example code
3. Terminology • A priority value is a value assigned to an item which indicates its priority  Usually used in a priority queue
4. Terminology • A priority queue is a kind of queue, in which items are added in order of occurrence, but removed according to their priority value  The item with the largest value is removed first
5. Terminology • For example, patients at a hospital are put into a priority queue with the most urgent patient at the beginning of the queue
6. Priority Queue Implementation • A priority queue can be implemented in many ways  For example, a linked list could be used  The item would be inserted in descending order  The largest item would be at the beginning of the list
7. Priority Queue Implementation • Or, a binary tree could be used  The item would be inserted into the binary tree  The largest item would be at the rightmost node • Typically, a heap is used to implement a priority queue
8. Heap & HeapException Code • See Heap.java for code  This is an array-based heap • Data fields • MAX_ARRAY_SIZE, indexOfLastElement, array • Public methods • Heap, toString, empty, add, get, remove, and main
9. Heap in Memory • Instantiating a Heap object will call the constructor, which initializes the data fields public Heap() { } • Data fields: private final int MAX_ARRAY_SIZE = 100; private int indexOfLastElement = -1; private T array[] = (T[]) new Object[MAX_ARRAY_SIZE];
10. Heap in Memory • Instantiate a Heap object (of Integers) Heap<Integer> heap = new Heap<Integer>(); heap index: 0 1 2 3 4 5 6 7 8 9 element: | | | | | | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 -1
11. Method add() in Memory • Add 8 to heap heap.add(8); heap index: 0 1 2 3 4 5 6 7 8 9 element: | | | | | | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 -1
12. Method add() in Memory indexOfLastElement++; array[indexOfLastElement] = item; heap index: 0 1 2 3 4 5 6 7 8 9 element: | 8| | | | | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 0
13. Method add() in Memory heap.add(6); heap.add(7); heap index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 6| 7| | | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 2
14. Method add() in Memory • Add 9 to heap and show “trickle up” heap.add(9); heap index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 6| 7| | | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 2
15. Method add() in Memory indexOfLastElement++; array[indexOfLastElement] = item; heap index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 6| 7| 9| | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 3
16. Method add() in Memory int indexOfChild = indexOfLastElement; int indexOfParent = (indexOfChild - 1) / 2; heap indexOfChild indexOfParent index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 6| 7| 9| | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 3 3 1
17. Method add() in Memory this.trickleUp(indexOfParent,indexOfChild); private void trickleUp(int indexOfParent, int indexOfChild) { heap indexOfChild indexOfParent index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 6| 7| 9| | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 3 3 1
18. Method add() in Memory if ((indexOfParent >= 0) && (compare(array[indexOfParent], array[indexOfChild]) < 0)) { heap indexOfChild indexOfParent index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 6| 7| 9| | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 3 3 1
19. Compare Method • Since arrays as a whole cannot be cast to java.lang.Comparable each element being compared is individually cast to java.lang.Comparable  The compare() method casts the parameter to java.lang.Comparable, and then calls the compareTo() method for that particular variable’s class
20. Method compare() Code • Method that compares two items  item1 = 6, item2 = 9  result = 6 – 9 = -3 private int compare(T item1, T item2) { java.lang.Comparable itemOne = (java.lang.Comparable) item1; int result = itemOne.compareTo(item2); return result; }
21. Method add() in Memory T temporary = array[indexOfParent]; temporary heap indexOfChild indexOfParent index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 6| 7| 9| | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 3 3 1 6
22. Method add() in Memory array[indexOfParent] = array[indexOfChild]; temporary heap indexOfChild indexOfParent index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 9| 7| 9| | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 3 3 1 6
23. Method add() in Memory array[indexOfChild] = temporary; temporary heap indexOfChild indexOfParent index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 9| 7| 6| | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 3 3 1 6
24. Method add() in Memory indexOfChild = indexOfParent; temporary heap indexOfChild indexOfParent index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 9| 7| 6| | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 3 1 1 6
25. Method add() in Memory indexOfParent = (indexOfChild – 1)/2 temporary this.trickleUp(indexOfParent, indexOfChild); heap indexOfChild indexOfParent index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 9| 7| 6| | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 3 1 0 6
26. Method add() in Memory if ((indexOfParent >= 0) && (compare(array[indexOfParent],array[indexOfChild]) < 0)) { heap indexOfChild indexOfParent index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 9| 7| 6| | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 3 1 0
27. Method compare() Code • Method that compares two items  item1 = 8, item2 = 9  result = 8 – 9 = -1 private int compare(T item1, T item2) { java.lang.Comparable itemOne = (java.lang.Comparable) item1; int result = itemOne.compareTo(item2); return result; }
28. Method add() in Memory T temporary = array[indexOfParent]; temporary heap indexOfChild indexOfParent index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 9| 7| 6| | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 3 1 0 8
29. Method add() in Memory array[indexOfParent] = array[indexOfChild]; temporary heap indexOfChild indexOfParent index: 0 1 2 3 4 5 6 7 8 9 element: | 9| 9| 7| 9| | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 3 1 0 8
30. Method add() in Memory array[indexOfChild] = temporary; temporary heap indexOfChild indexOfParent index: 0 1 2 3 4 5 6 7 8 9 element: | 9| 8| 7| 6| | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 3 1 0 8
31. Method add() in Memory indexOfChild = indexOfParent; temporary heap indexOfChild indexOfParent index: 0 1 2 3 4 5 6 7 8 9 element: | 9| 8| 7| 6| | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 3 0 0 8
32. Method add() in Memory indexOfParent = (indexOfChild - 1) / 2; temporary this.trickleUp(indexOfParent, indexOfChild); heap indexOfChild indexOfParent index: 0 1 2 3 4 5 6 7 8 9 element: | 9| 8| 7| 6| | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 3 0 0 8
33. Method get() • Gets an item from the top of the heap  Returns an address (pointer) to the element at array index zero • Example method call: • int top = heap.get();
34. Method get() in Memory T root = array[0]; return root; heap root index: 0 1 2 3 4 5 6 7 8 9 element: | 9| 8| 7| 6| | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 3
35. Method get() in Memory int top = heap.get(); heap top index: 0 1 2 3 4 5 6 7 8 9 element: | 9| 8| 7| 6| | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 3
36. Method remove() in Memory int next = heap.remove(); heap index: 0 1 2 3 4 5 6 7 8 9 element: | 9| 8| 7| 6| 5| 4| 3| | | | MAX_ARRAY_SIZE indexOfLastElement array 100 6
37. Method remove() in Memory T root = array[0]; array[0] = array[indexOfLastElement]; heap root index: 0 1 2 3 4 5 6 7 8 9 element: | 3| 8| 7| 6| 5| 4| 3| | | | MAX_ARRAY_SIZE indexOfLastElement array 100 6 9
38. Method remove() in Memory indexOfLastElement--; this.trickleDown(0); heap root index: 0 1 2 3 4 5 6 7 8 9 element: | 3| 8| 7| 6| 5| 4| | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 5 9
39. Method remove() in Memory int indexOfLeftChild = 2 * indexOfParent + 1; int indexOfRightChild = 2 * indexOfParent + 2; heap indexOfParent indexOfLeftChild indexOfRightChild index: 0 1 2 3 4 5 6 7 8 9 element: | 3| 8| 7| 6| 5| 4| | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 5 1 0 2
40. Method remove() in Memory int indexOfLargestOfThreeNodes=indexOfParent; heap indexOfParent indexOfLeftChild indexOfRightChild indexOfLargestOfThreeNodes index: 0 1 2 3 4 5 6 7 8 9 element: | 3| 8| 7| 6| 5| 4| | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 5 1 0 2 0
41. Method remove() in Memory //calculate index of largest of 3 nodes indexOfParent heap indexOfLeftChild indexOfRightChild indexOfLargestOfThreeNodes index: 0 1 2 3 4 5 6 7 8 9 element: | 3| 8| 7| 6| 5| 4| | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 5 1 0 2 1
42. Method remove() in Memory //swap parent with largest child indexOfParent heap indexOfLeftChild indexOfRightChild indexOfLargestOfThreeNodes index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 3| 7| 6| 5| 4| | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 5 1 0 2 1
43. Method remove() in Memory this.trickleDown(indexOfLargestOfThreeNodes); indexOfParent heap indexOfLeftChild indexOfRightChild indexOfLargestOfThreeNodes index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 3| 7| 6| 5| 4| | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 5 1 0 2 1
44. Method remove() in Memory int indexOfLeftChild = 2 * indexOfParent + 1; indexOfParent int indexOfRightChild = 2 * indexOfParent + 2; heap indexOfLeftChild indexOfRightChild index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 3| 7| 6| 5| 4| | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 5 3 1 4
45. Method remove() in Memory indexOfParent int indexOfLargestOfThreeNodes = indexOfParent; heap indexOfLeftChild indexOfRightChild indexOfLargestOfThreeNodes index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 3| 7| 6| 5| 4| | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 5 3 1 4 1
46. Method remove() in Memory //calculate index of largest of 3 nodes indexOfParent heap indexOfLeftChild indexOfRightChild indexOfLargestOfThreeNodes index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 3| 7| 6| 5| 4| | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 5 3 1 4 3
47. Method remove() in Memory //swap parent with largest child indexOfParent heap indexOfLeftChild indexOfRightChild indexOfLargestOfThreeNodes index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 6| 7| 3| 5| 4| | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 5 3 1 4 3
48. Method remove() in Memory this.trickleDown(indexOfLargestOfThreeNodes); indexOfParent heap indexOfLeftChild indexOfRightChild indexOfLargestOfThreeNodes index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 6| 7| 3| 5| 4| | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 5 3 1 4 3
49. Method remove() in Memory int indexOfLeftChild = 2 * indexOfParent + 1; indexOfParent int indexOfRightChild = 2 * indexOfParent + 2; heap indexOfLeftChild indexOfRightChild index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 6| 7| 3| 5| 4| | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 5 7 3 8
50. Method remove() in Memory return root;} int next = heap.remove(); heap next root index: 0 1 2 3 4 5 6 7 8 9 element: | 8| 6| 7| 3| 5| 4| | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 5 9
51. Heap main() Method • See the main() method for example code that instantiates a Heap object and calls the methods of the class  See the last method in Heap.java  For output, see the toString() method
52. Example Code • QueueInterface interface  See QueueInterface.java  An interface is a list of method prototypes  Queue methods: empty(), offer(), poll(), peek()
53. Example Code • PriorityQueue class  See PriorityQueue.java  This priority queue contains a heap & calls the heap’s methods  Same method names for Queue class, but a PriorityQueue (first-in highest-out) works slightly different than a Queue (first-in last-out)
54. PriorityQueue in Memory • Instantiating a PriorityQueue object will call the constructor, which initializes the data fields public PriorityQueue() { } • Data fields: private Heap<T> heap = new Heap<T>();
55. PriorityQueue in Memory • PriorityQueue object (of Integers) QueueInterface<Integer> queue = new PriorityQueue<Integer>(); queue index: 0 1 2 3 4 5 6 7 8 9 element: | | | | | | | | | | | MAX_ARRAY_SIZE indexOfLastElement array 100 -1 heap
56. PriorityQueue & Heap Methods • Each PriorityQueue method calls the corresponding Heap method
57. PriorityQueue & Heap Methods • PriorityQueue  empty()  offer(T element)  poll()  peek() • Heap methods  heap.empty()  heap.add(element)  heap.remove()  heap.get()
58. PriorityQueue main() Method • See the main() method for example code that instantiates a PriorityQueue object and calls the methods of the class  See the last method in PriorityQueue.java
59. Memory Defragmenter • Priority queues • Heap implementation • Example code
60. Task Manager • Before the next class, you need to: 1.Do the assignment corresponding to this lecture 2.Email me any questions you may have about the material 3.Turn in the assignment before the due date 4.Eat some grits!